Examining the Types of Mathematical Tasks Used to Explore the Mathematics Instruction by Elementary School Teachers

Wei-Min Hsu

doi:10.4236/ce.2013.46056

Abstract

This study examined the different types of mathematical tasks used in the classroom to explore the nature of mathematics instruction of three sixth grade teachers in an elementary school. Case studies, instructional observations, and classroom artifacts were used to collect data. The results showed that the three teachers used different types of mathematical tasks and implementation methods. One teacher focused on high cognitive demand tasks, most of which involved substantial group discussion and students working cooperatively. Even though the other two also used many high cognitive demand tasks, these were mainly presented via teacher-student dialogue. By examining the types of mathematical tasks and their implementation, it was found that the group discussion tasks were generally all high cognitive demand tasks, in which the students fully explained the solution process. As for the tasks administered through teacher-student dialogue, due to the usage of large amounts of closed-ended dialogue, the students used low cognition to solve the mathematical tasks and did not have the opportunity to completely explain their thinking about the solutions. Thus, in order to fully understand the nature of mathematics instruction by teachers, there should be simultaneous consideration of the types of mathematical tasks used as well as how the tasks were implemented.

Highlights

Mathematics instruction in the classroom is the key to understanding student learning in mathematics (Boaler & Staples, 2008; Gutstein, 2003; Henningsen & Stein, 1997; Mullis, Martin, Gonzales, & Chrostowski, 2004; Stein, Remillard, & Smith, 2007)
Lian was the most inclined toward conforming to mathematics instruction policy recommendations, including adopting mathematical tasks with high cognitive demands, using open questions to interact with the students, and giving the students opportunities to think and express their understanding
Of the mathematical tasks implemented by Mike and Yan, their instruction generally caused the students to learn mathematical tasks with low cognitive demand methods implemented by close dialogue

Summary

Introduction

Mathematics instruction in the classroom is the key to understanding student learning in mathematics (Boaler & Staples, 2008; Gutstein, 2003; Henningsen & Stein, 1997; Mullis, Martin, Gonzales, & Chrostowski, 2004; Stein, Remillard, & Smith, 2007). Hiebert and Grouws (2007) believed that instruction is comprised of student-teacher interactions in the classroom based on the learning of content, and that the purpose of teacher-student interaction is to achieve specific learning objectives. Seen from this perspective, there are two key focuses of classroom mathematics instruction, the first is the learning content and the second is the interaction between teachers and students regarding the content. It is clear that mathematics instruction in the classroom focuses on mathematical tasks, and the implementation of these tasks typically involves teacher-student interaction in order to facilitate mathematics learning. The implementation of mathematical tasks in the classroom is a productive way to explore the mathematics instruction of teachers

Methods

Results

Conclusion